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Remark on compactifications of metrizable spaces

Authors
Journal
Topology and its Applications
0166-8641
Publisher
Elsevier
Publication Date
Volume
15
Issue
3
Identifiers
DOI: 10.1016/0166-8641(83)90059-7

Abstract

Abstract We show that for a given metrizable separable space X and a family{ f i }; ∞ i=1 of continuous functions of X into X the set of all continuous embeddings h of the space X into the Hilbert cube I ω such that all functions hf i h -1 are extendable to continuous functions f ̃ i: h(X)) → h(X) contains a dense G δ-set in the function space C( X, I ω). This strengthens and gives a new proof of some earlier results of Engelking, de Groot and McDowell.

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